Bracket terms
Bracket terms are one author`s notation that denote the different sum of the squares of the standard deviations. Since there are many different standard deviations from the many different groups of subjects within any single ANOVA test, there are many different ways to "represent" these sums of squares as mathematical formulas, which is what they truly represent. The name "bracket" refers to the many individual calculations necessary which are all very nicely added together within the final "bracket".
Example:
ANOVA Table
or, in other words...
[A] Add up the measurements in each group first, then square each
group total, add all of the squared totals together, and then divide
by the number of measurements in a single group.
or, in other words...
[Y] Square all of the measurements, regardless of which group that they
are in, then add them all up.
[T] = T2/an or, in other words...
[T] Add up the measurements in each group first, then add those sums
together, then square that number, then divide that number by the
total number of measurements in all groups.
*Important note: do not confuse the division process of finding a bracket term value with finding the mean square process when didving the bracket term by the degrees of freedom! They are very similar, but different!
Example: Three groups of patients were given different doses of a new drug (the Algebra Pill) that is supposed to increase their algebra skills. They took an exam with a possible score of 20. Assume that all participants were selected at random.
[A] = [(12+8+7+5)2 + (10+19+10+11)2 + (14+12+10+12)2]
divided by 4 = 5828/4 = 1457
[Y] = [122+82+72+52+102+192+102+112+42+122+102+122]
divided by 1 = 1548
[T] = [(12+8+7+5+10+19+10+11+14+12+10+12]2
divided by (4x3) = 16,900/12 = 1408
**Important note: then these bracket term values would be divided by each of their corresponding degrees of freedom fo find the mean squares.
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